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Proof step 3 from proof inv-unmap (previous step)

sb.main + # lpt = # avol, avol[0] = mapped(buf), avol[sb.orph] = mapped(buf0), avol[sb.log] = mapped(buf1), m < # lpt, disk-layout(sb, # lpt), ebm-vol-inv(avol), is-encoded(log, buf1), is-encoded(lpt, lebs(avol, sb.lpt, lptlebs(# lpt, LEB_SIZE))), is-encoded(sb, buf), is-encoded-pad(orphans, sb.orphsize, buf0), mapped-full?(avol, sb.lpt, lptlebs(# lpt, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪persistence_io_unmap#(m, sb; avol)⟫ ( (∃ lpt0, log, orphans. disk-layout(sb, # lpt0) ∧ sb.main + # lpt0 = # avol ∧ avol[0].mapped? ∧ is-encoded(sb, avol[0].data) ∧ avol[sb.orph].mapped? ∧ is-encoded-pad(orphans, sb.orphsize, avol[sb.orph].data) ∧ avol[sb.log].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[sb.log].data = logoff) ∧ is-encoded(log, avol[sb.log].data) ∧ mapped-full?(avol, sb.lpt, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol, sb.lpt, lptlebs(# lpt0, LEB_SIZE)))) ∧ ebm-vol-inv(avol))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
m5 + # lpt = # avol, avol[m1] = mapped(buf1), avol[m2] = mapped(buf0), avol[0] = mapped(buf), sb = mksb(adr, m0, m1, m2, m3, m4, m5), m < # lpt, disk-layout(sb, # lpt), ebm-vol-inv(avol), is-encoded(sb, buf), is-encoded(lpt, lebs(avol, m4, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf1), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol, m4, lptlebs(# lpt, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪persistence_io_unmap#(m, sb; avol)⟫ ( (∃ lpt0, log, orphans. disk-layout(sb, # lpt0) ∧ m5 + # lpt0 = # avol ∧ avol[0].mapped? ∧ is-encoded(sb, avol[0].data) ∧ avol[m2].mapped? ∧ is-encoded-pad(orphans, m3, avol[m2].data) ∧ avol[m1].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[m1].data = logoff) ∧ is-encoded(log, avol[m1].data) ∧ mapped-full?(avol, m4, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol, m4, lptlebs(# lpt0, LEB_SIZE)))) ∧ ebm-vol-inv(avol))

Rule argument

spec: superblock name: elim seq: ⊦ ( ( ( ( (adr = sb.indexaddr ∧ m = sb.maxino) ∧ m0 = sb.log) ∧ m1 = sb.orph) ∧ m2 = sb.orphsize) ∧ m3 = sb.lpt) ∧ m4 = sb.main ↔ sb = mksb(adr, m, m0, m1, m2, m3, m4) subst: [sb, adr, m, m0, m1, m2, m3, m4] → [sb, adr, m0, m1, m2, m3, m4, m5]

Additional information

Used simplifier rules: ⊦ ( ( ( ((adr = sb.indexaddr ∧ m = sb.maxino) ∧ m0 = sb.log) ∧ m1 = sb.orph) ∧ m2 = sb.orphsize) ∧ m3 = sb.lpt) ∧ m4 = sb.main ↔ sb = mksb(adr, m, m0, m1, m2, m3, m4); (elim) Used terms: sb, adr, m0, m1, m2, m3, m4, m5